Question: The geometric sequence $(a_i)$ is defined by the formula: $a_1 = -\dfrac{5}{16}$ $a_i = 4a_{i-1}$ What is $a_{2}$, the second term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $-\dfrac{5}{16}$ and the common ratio is $4$ The second term is simply the first term times the common ratio. Therefore, the second term is equal to $a_2 = -\dfrac{5}{16} \cdot 4 = -\dfrac{5}{4}$.